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Dear fellow Marvel Avengers: Addict,

Wouldn't you like to know the statistical effect of switching hero uniforms? Is attack truly the best PVP stat? Imagine what if we could statistically determine what drives PVP ratings over time. Basically everything that can be measured will be measured and regressed to determine its effect on rating throughout the season (I don't know how to do time-series regressions but I could ask around for help).

Please click the link below to contribute 

https://docs.google.com/forms/d/15czWHWtJqw30XFHkuRImV1zddAGoPbnqg60NmN9T9cs/viewform.

This will take less than 5 minutes I promise, and you will be glad you contributed! Knowledge is power. Power is winning.

Hypotheses

The first step is to build a hypothetical model to determine what drives ratings. Thanks to PKB, Caslandr and many other notable suggestors, we have

vctaae.png

We believe that PVP end-season rating is driven by the intercept 800 in the ELO system, and increases with HP, Attack, Defence, Accuracy, and Evasion, because obviously people with higher stats should rise to the level of their gameplay. The term "number fights initiated" is important because attacking more can increase ratings beyond what stats alone would suggest.

There are two factors. 1. The ELO system matches people of similar levels, and thus the distribution of ratings around any given level bracket should be very similar in mean and variance. 2. Higher levels obviously have more stats, so we must correct for this (with fixed effects and whatnot).

This is obviously a simplified model without time series effects because longditudinal data collection and interpretation would be too onerous. We do not account for team composition because it is extremely difficult to regress these "categorical variables".

i =800+β1HP+β2Attack+β3Defence+β4Accuracy+β5Evasion+β6 number fights initiated+errorterm

i

Ratingi =800+β1HP+β2Attack+β3Defence+β4Accuracy+β5Evasion+β6 number fights initiated+errorterm Ratingi =800+β1HP+β2Attack+β3Defence+β4Accuracy+β5Evasion+β6 number fights initiated+errortermi

Methodology

gi =800+β1HP+β2Attack+β3Defence+β4Accuracy+β5Evasion+β6 number fights initiated+errorterm

i

On Feb 4 2014, the end of PVP Season 13, I collected data on every one of my allies, including other players whom I had faced in the battle logs. The rest of the sample comes from responses to my survey above. The data collected were rating, level, all the stats on their profile page. To scale armory numbers into actual stats, these data were then transformed using an estimated interpolation formula. These were then aggregated into total statistics. For example, Total HP (tothp) = total hero bonus + armory HP (interpolated). This does not include the "base HP" of the hero.

Cool regression statistics

Here is the scatterplot of key stats not including HP since HP does not fit well on the scale. Stats are increasing with level according to some sort of power curve. From cubic-polynomial approximation,

Base stat = -5E-05Level3 + 0.0379Level2 + 13.905Level + 63.973

300yzpe.png

Here is a log scatterplot of all the five key stats on level. Note the large cluster around Level 70. That is because I collect stats from both offensive and defensive battles, and those players are around the Level 70 Adamantium range.

jjlg81.png

Here's the regression on all stats, full sample. Level is negatively correlated with rating and significant. This is pure sampling bias: I have few high ranked players Level 80 - 300 because I don't face them in PVP. I have tons of high ranked players in Level 70s because those is whom I face. HP and Attack are positively correlated and significant. Defence is negatively correlated, surprising. Accuracy and evasion have no significant effect.</p>

2vudog3.png

Here's the regression for 1550+ (very highly-ranked players comprising top 0.7% of the population . All variables lose significance, meaning among our high ranked players, the variation in the statistics does not well-explain rating. That is why we need more data from all players, of all levels!

 24g3zgk.png

Fixed effects (level) controls for the different player levels. HP and Attack positively correlated. Defence and Accuracy negatively. Evasion not significant.

nq5jrm.jpg

Thank you for reading all this. The conclusion is that attack and health significantly affect PVP ratings, defence and accuracy are negatively correlated which is strange. After all, higher statistics should (in theory) contribute to more ratings. Perhaps there are other confounding factors.

TLDR; Please click the link below to contribute 

https://docs.google.com/forms/d/15czWHWtJqw30XFHkuRImV1zddAGoPbnqg60NmN9T9cs/viewform.

This will take less than 5 minutes I promise, and you will be glad you contributed! Knowledge is power. Power is winning.

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